Application of numerical filtration methods in problems of integration and series summing

Abstract

In this paper, some extrapolation methods are considered and numerical experiments are performed. In particular, the results obtained by different integration methods are compared. The convergence of the series is also accelerated in foundation of the sum. The Richardson and the Aitken extrapolation methods are applied to refine the numerical results.  The analysis of numerical filtration results allows estimating its high accuracy.